A Hybrid Model for Assessing Student Mathematical Skills
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
1 - Department of Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Sciences Institute of Western Greece, Patras, Greece.
کلید واژه: Neutrosophic set (NS), Fuzzy set (FS), Fuzzy logic (FL), Soft set (SS), Grey number (GN), COG defuzzification technique, Rectangular fuzzy assessment model (RFAM), GPA index,
چکیده مقاله :
Student assessment is a very important process in education, because it helps the instructor to determine student mistakes and to improve their performance by reforming his/her teaching plans. A hybrid assessment method using qualitative grades for evaluating student mathematical skills is presented in this work. The paper starts with the mathematical background which is necessary for the understanding of its contents. This includes basic information about fuzzy, neutrosophic and soft sets, and about grey numbers. It also includes a description of the use of the center of gravity (COG) defuzzification technique for assessing a student group’s quality performance. The COG technique is compared with the classical method of calculating the GP A index. The hybrid assessment method, which is based on all the previous concepts and processes, is developed next and the article closes with the final conclusion and some recommendations for future research.
Student assessment is a very important process in education, because it helps the instructor to determine student mistakes and to improve their performance by reforming his/her teaching plans. A hybrid assessment method using qualitative grades for evaluating student mathematical skills is presented in this work. The paper starts with the mathematical background which is necessary for the understanding of its contents. This includes basic information about fuzzy, neutrosophic and soft sets, and about grey numbers. It also includes a description of the use of the center of gravity (COG) defuzzification technique for assessing a student group’s quality performance. The COG technique is compared with the classical method of calculating the GP A index. The hybrid assessment method, which is based on all the previous concepts and processes, is developed next and the article closes with the final conclusion and some recommendations for future research.
[1] K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
[2] J. Deng, Control Problems of Grey Systems, Systems and Control Letters, (1982), 288-294.
[3] J. Deng, Introduction to Grey System Theory, The Journal of Grey System, 1 (1989), 1-24.
[4] D. Dubois and H. Prade, Interval-Valued Fuzzy Sets, Possibility Theory and Imprecise Probability, Proceedings EUSFLAT-LFA, (2005), 314-319.
[5] D. Dubois and H. Prade, Possibility theory, probability theory and multiple-valued logics: A clarification, Ann. Math. Artif. Intell., 32 (2001), 35-66.
[6] D. Dubois and H. Prade, Possibility Theory and its Applications: a Retrospective and Prospective view. In: Della Riccia, G. Dubois, D. Kruse, R. Lenz, H. J. (eds) Decision Theory and Multi-Agent Planning. CISM International Centre for Mechanical Sciences, Springer, Vienna, 482 (2006), 89-109.
[7] J. Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic sets, intuitionistic fuzzy sets and topologies, Fuzzy Sets and Systems, 156 (2005), 445-484.
[8] G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, (1988).
[9] P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications, 45 (2003), 555-562.
[10] D. Molodtsov, Soft Set Theory first results, Computers and Mathematics with Applications, 37(4-5) (1999), 19-31.
[11] R. A. Moore, R. B. Kearfort and M. G. Clood, Introduction to Interval Analysis, 2nded., SIAM, Philadelphia, PA, USA, (1995).
[12] Z. Pawlak, Rough Sets: Aspects of Reasoning about Data, Kluer Academic Publishers, Dordrecht, (1991).
[13] F. G. Shi and C. Z. Fan, Fuzzy soft sets as L-fuzzy sets, Journal of Intelligent & Fuzzy Systems, 37 (2019).
[14] F. Smarandache, Neutrosophy / Neutrosophic Probability, Set, and Logic, Proquest, Michigan, USA, (1998).
[15] F. Smarandache, Subtraction and Division of Neutrosophic Numbers, Critical Review, 13 (2016), 103-110.
[16] I. Ya. Subbotin, H. Badkoobehi and N.N. Bilotckii, Application of fuzzy logic to learning assessment, Didactics of Mathematics: Problems and Investigations, 22 (2004), 38-41.
[17] M. Gr. Voskoglou, The process of learning mathematics : A Fuzzy Sets approach, Millenium- Revista do I.S.P.V., 17 (2000), 272-279.
[18] M. Gr. Voskoglou, Fuzziness or probability in the process of learning: A general question illustrated by examples from teaching mathematics, The Journal of Fuzzy Mathematics, 17(3) (2009), 679-686.
[19] M. Gr. Voskoglou, Finite Markov Chain and Fuzzy Logic Assessment Models: Emerging Research and Opportunities, Createspace independent publishing platform (Amazon), Columbia, SC, (2017).
[20] M. Gr. Voskoglou, Methods for Assessing Human-Machine Performance under Fuzzy Conditions, Mathematics, 7(230) (2019).
[21] M. Gr. Voskoglou, Generalizations of Fuzzy Sets and Relative Theories, in M. Voskoglou (Ed.), An Essential Guide to Fuzzy Systems, Nova Science Publishers, NY, (2019), 345-353.
[22] M. Gr. Voskoglou, Application of soft sets to assessment processes, American Journal of Applied Mathematics and Statistics, 10(1) (2022), 1-3.
[23] M. Gr. Voskoglou, A Hybrid Model for Decision Making Utilizing TFNs and Soft Sets as Tools, Equations, 2 (2022), 65-69.
[24] M. Gr. Voskoglou, A Combined Use of Soft Sets and Grey Numbers in Decision Making, Journal of Computational and Cognitive Engineering, (2022), 1-4.
[25] M. Gr. Voskoglou and S. Broumi, A Hybrid Method for the Assessment of Analogical Reasoning Skills, Journal of Fuzzy Extension and Applications, 3(2) (2022), 152-157.
[26] M. Gr. Voskoglou, S. Broumi and F. Smarandache, A combined use of soft and neutrosophic sets for student assessment with qualitative grades, Journal of Neutrosophic and Fuzzy Systems, 4(1) (2022), 15-20.
[27] H. Wang, F. Smarandanche, Y. Zhang, and R. Sunderraman, Single Valued Neutrosophic Sets, Review of the Air Force Academy (Brasov), 1(16) (2010), 10-14.
[28] L. A. Zadeh, Fuzzy Sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1 (1978), 3-28.
[29] L. A. Zadeh, Fuzzy Sets, Inf. Control, 8 (1965), 338-353.
[30] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern., 3 (1973), 28-44.
